Chapter 3.3, Problem 51PPS

(a)

To determine

To Find:The product using the number line.

Answer to Problem 51PPS

  

Explanation of Solution

Given:The expression $\frac{1}{2}\times 4$ mean $\frac{1}{2}of4$ . The number line shows the product of $\frac{1}{2}$ and $4$ is $2$ . Find each product using the number line.

  $\frac{2}{3}of6$

Given: $\frac{2}{3}of6$

The product of $\frac{2}{3}of6$ is $4$

The number line showing the product is

  

(b)

To determine

To Find: The product using the number line

Answer to Problem 51PPS

  

Explanation of Solution

Given: The expression $\frac{1}{2}\times 4$ mean $\frac{1}{2}of4$ . The number line shows the product of $\frac{1}{2}$ and $4$ is $2$ . Find each product using the number line

  $\frac{3}{4}of8$

Given: $\frac{3}{4}of8$

The product of $\frac{3}{4}of8$ is $6$

The product on the number line is

  

(c)

To determine

To Find: The product using the number line

Answer to Problem 51PPS

  

Explanation of Solution

Given: The expression $\frac{1}{2}\times 4$ mean $\frac{1}{2}of4$ . The number line shows the product of $\frac{1}{2}$ and $4$ is $2$ . Find each product using the number line

  $\frac{1}{2}of\frac{2}{3}$

Given: $\frac{1}{2}of\frac{2}{3}$

The product of $\frac{1}{2}of\frac{2}{3}$ is $\frac{1}{3}$

The product on the number line is

  

(d)

To determine

To Find: The product using the number line

Answer to Problem 51PPS

  

Explanation of Solution

Given: The expression $\frac{1}{2}\times 4$ mean $\frac{1}{2}of4$ . The number line shows the product of $\frac{1}{2}$ and $4$ is $2$ . Find each product using the number line

  $\frac{1}{2}of2$

Given: $\frac{1}{2}of2$

The product of $\frac{1}{2}of2$ is $1$

The product on the number line is

  

(e)

To determine

To Find: The product using the number line

Answer to Problem 51PPS

  

Explanation of Solution

Given: The expression $\frac{1}{2}\times 4$ mean $\frac{1}{2}of4$ . The number line shows the product of $\frac{1}{2}$ and $4$ is $2$ . Find each product using the number line

  $\frac{2}{3}of\frac{3}{2}$

Given: $\frac{2}{3}of\frac{3}{2}$

The product of $\frac{2}{3}of\frac{3}{2}$ is $1$

The product on the number line is

  

(f)

To determine

To Find: The product using the number line

Answer to Problem 51PPS

  

Explanation of Solution

Given: The expression $\frac{1}{2}\times 4$ mean $\frac{1}{2}of4$ . The number line shows the product of $\frac{1}{2}$ and $4$ is $2$ . Find each product using the number line

  $\frac{3}{7}of\frac{7}{3}$

Given: $\frac{3}{7}of\frac{7}{3}$

The product of $\frac{3}{7}of\frac{7}{3}$ is $1$

The product on the number line is

  

(h)

To determine

To Find:The pattern

Answer to Problem 51PPS

The fractions that were multiplied are the reciprocal of each other and therefore the result is $1$

Explanation of Solution

Given: Look back to the solutions for exercise d and f. what pattern do you notices.

It is noticed that the fractions that were multiplied are the reciprocal of each other and therefore the result is $1$

(i)

To determine

To Find: The Product of $\frac{a}{b}\cdot \frac{b}{a}$

Answer to Problem 51PPS

  $1$

Explanation of Solution

Given: What is the product of $\frac{a}{b}\cdot \frac{b}{a}$ where $a,b\ne 0$

The fractions that were multiplied are the reciprocal of each other and therefore the result is $1$

Therefore

  $\frac{a}{b}\cdot \frac{b}{a}=1$